This paper considers the problem of modeling migraine severity assessments and their dependence on weather and time characteristics. Since ordinal severity measurements arise from a single patient dependencies among the measurements have to be accounted for. For this the autoregressive ordinal probit (AOP) model of M¨uller and Czado (2004) is utilized and fitted by a grouped move multigrid Monte Carlo (GM-MGMC) Gibbs sampler. Initially, covariates are selected using proportional odds models ignoring this dependency. Model fit and model comparison are discussed. The analysis shows that humidity, windchill, sunshine length and pressure differences have an effect in addition to a high dependence on previous mea- surements. A comparison with proportional odds specifications shows that the AOP models are preferred.
Proportional odds autoregressive component ordinal valued time series regression Markov Chain Monte Carlo (MCMC) deviance